Scuffles erupted outside Alexandria's Al-Qaed Ibrahim Mosque after noon prayers on Friday when local residents attacked dozens of supporters of former president Mohamed Morsi.
Stones were thrown back and forth between the groups, Al-Ahram Arabic news website reported.
The National Alliance to Support Legitimacy, led by Morsi's Muslim Brotherhood, called for demonstrations on Friday to press for Morsi's reinstatement and other key demands.
The alliance condemned Thursday's bomb attack against Interior Minister Mohamed Ibrahim and reiterated its call for protests to remain peaceful.
A security crackdown on pro-Morsi protest camps in Cairo on 14 August left hundreds dead and sparked days of intense violence nationwide. Intermittent clashes have been ongoing between Morsi supporters and anti-Brotherhood civilians.